1 mark, −0.333MicroeconomicsGeneral equilibrium and exchange economiesWalras' law, numeraire and relative pricesModerateabout 1 min

GATE 2021 Question 10: General equilibrium and exchange economies

Walras' Law implies that if there are $N$ markets in the economy, then one only needs to find equilibrium prices in

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Answer and worked solution

Answer: (B)

Walras' Law states that the value of aggregate excess demand across all markets in the economy sums to zero identically (a consequence of every agent's budget constraint holding with equality). Formally, if $Z_i$ is the excess demand in market $i$ , then $\sum_{i=1}^N p_i Z_i \equiv 0$ for any set of prices, not just equilibrium prices.

This means that if $N-1$ of the $N$ markets are in equilibrium (each with zero excess demand), the $N$ -th market's excess demand must also be zero automatically, since the sum across all $N$ must equal zero. So one only needs to independently verify/solve for equilibrium prices in $N-1$ markets — the last one is guaranteed to clear as a consequence.

Therefore the answer is (B) $N-1$ markets.

The trap: (D) all the

N

markets

Students who don't specifically recall Walras' Law's implication may default to assuming all $N$ markets need independent verification (the naive answer), missing the economy-wide budget-constraint logic that makes one market's equilibrium redundant to check.

Plain-text version

Walras' Law implies that if there are N markets in the economy, then one only needs to find equilibrium prices in (A) N-2 markets (B) N-1 markets (C) N+1 markets (D) all the N markets

General equilibrium and exchange economies has come up 69 times in 7 exams since 2004.

What this question tests

This question is on Walras' law, numeraire and relative prices, part of General equilibrium and exchange economies in Microeconomics.

Why one market clears automatically when the others do, and why only relative prices matter.

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